Local linear smoothers in regression function estimation

A method based on local linear approximation is used to estimate the mean regression function. The proposed local linear smoother has several advantages in comparison with other linear smoothers. Motivated by this fact, we follow this approach to estimate more general functions, among which, conditional median and conditional quantile functions. A further generalization involves the estimation of high-dimensional regression functions. In particular, additive and two-term interaction nonparametric regression models are discussed. This allows us to deal with the problem of "curse of dimensionality". Algorithms are provided to fit these models.

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